In this paper, we employ the Lyapunov theory to generalize the finite time stability (FTS) results from general deterministic impulsive systems to impulsive stochastic time-varying systems, which overcomes inherent challenges. Sufficient conditions for the FTS of the system under stabilizing and destabilizing impulses are established by using the method of average dwell interval (ADT). For FTS of stabilizing impulses, we relax the constraint on the differential operator by allowing it to be indefinite rather than strictly negative or semi-negative definite. Furthermore, the theoretical results are applied to impulsive stochastic neural networks. Finally, two numerical examples are given to validate the reliability and practicability of the obtained results.

中文翻译：

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非线性脉冲随机系统的有限时间稳定性及其在神经网络中的应用


在本文中，我们采用李亚普诺夫理论将一般确定性脉冲系统的有限时间稳定性（FTS）结果推广到脉冲随机时变系统，克服了固有的挑战。采用平均驻留间隔（ADT）方法建立了系统在稳定和不稳定脉冲作用下FTS的充分条件。对于稳定脉冲的 FTS，我们通过允许微分算子不定而不是严格负定或半负定来放宽对微分算子的约束。此外，理论结果应用于脉冲随机神经网络。最后给出两个数值算例验证了所得结果的可靠性和实用性。